In this paper we intend to establish fast numerical approaches to solve a class of initial-
boundary problem of time-space fractional convection–diffusion equations. We present a …

In this paper, we consider a two-sided space-fractional diffusion equation with variable
coefficients on a finite domain. Firstly, based on the nodal basis functions, we present a new …

We develop a monotone finite volume method for the time fractional Fokker-Planck
equations and theoretically prove its unconditional stability. We show that the convergence …

We present a survey of fractional differential equations and in particular of the computational
cost for their numerical solutions from the view of computer science. The computational …

We derive a finite volume method for two-sided fractional diffusion equations with Riemann–
Liouville derivatives in one spatial dimension. The method applies to non-uniform meshes …

The fractional reaction-diffusion equations play an important role in dynamical systems.
Indeed, it is time consuming to numerically solve differential fractional diffusion equations. In …

A time-fractional diffusion equation involving the Dirichlet energy is considered with nonlocal
diffusion operator in the space which has dimension d∈{2, 3} and the Caputo sense …

The aims of this paper are to investigate and propose a numerical approximation for a
quenching type diffusion problem associated with a two-sided Riemann-Liouville space …

We develop a unified Petrov–Galerkin spectral method for a class of fractional partial
differential equations with two-sided derivatives and constant coefficients of the form D t 2 τ 0 …

We develop a finite volume method to numerically solve the N-dimensional time fractional
Fokker–Planck equation ∂^ α ω ∂ t^ α= k_ α Δ ω-∑\limits _ k= 1^ N ∂ (f^(k) ω) ∂ x_k,∂ α …